Preheat oven to 350F and line two baking sheets with parchment paper.
Coat:
In a large bowl, whisk together the honey, Dijon mustard, ½ teaspoon salt, curry powder, and black pepper. Scoop a couple of tablespoons of the mixture in a small ramekin for basting the chicken legs.
Place the chicken legs into the bowl and toss to coat with the honey glaze. Make this with a basting brush or the back of a spoon. Transfer the chicken legs onto one of the lined baking sheets.
Bake the chicken:
Bake them in the preheated oven, for 1 hour, basting and turning them over half way through, until the chicken is browned and the internal temperature has reached 175F. Remove them from the oven when finished, cover in foil to keep warm.
Prep the carrots:
While the chicken is cooking, wash, peel, and cut carrots into strips. Toss carrots with olive oil and the remaining ½ teaspoon of salt in a large bowl.
Bake the chicken:
Turn oven up to 450F and bake the carrots for 10 minutes, until the thickest slices are golden and the tops are crispy.